量子色动力学（QCD）在高重子数密度时具有丰富的相结构和物理现象。本研究涉及处于非微扰密度区域的强耦合夸克物质，对于理解致密天体物理和丰重子重离子碰撞物理有重要意义。不幸的是，由于符号问题，第一原理格点QCD模拟计算还不能处理有限重子数密度。目前对于非微扰密度区域的理论研究主要采用基于真空唯象学的有效模型，而且广泛采用平均场近似等简单的多体理论方法，无法作出令人满意的理论预言。本项目将从QCD第一原理出发构造适用于非微扰密度区域的有效理论，并发展超越平均场近似的多体理论方法，紧密结合没有符号问题的类QCD理论在有限密度时的格点模拟结果来验证有效理论和多体理论方法的可靠性。在此基础上，本项目将系统的研究非微扰密度区域的相结构和物理性质，预言新的物理现象。本项目将极大的推进有限密度QCD物理的研究，并为研究致密星体和丰重子重离子碰撞物理提供坚实基础。

Quantum Chromodynamics (QCD) at high baryon density has rich phases and physical phenomena. This project concerns the strongly coupled quark matter in the nonperturbative density regime, which is of great significance for our understanding of the astrophysics of compact objects and the phenomenology of baryon-rich heavy ion collisions. Unfortunately, the first-principle lattice QCD simulation cannot treat a finite baryon density because of the sign problem. So far theoretical studies of the nonperturbative density regime mainly employ some effective models built based on vacuum phenomenology and use some simple many-body methods such as the mean-field approximation, which makes the theoretical predictions unconvincing. In this project, we will construct an effective theory which is applicable for the nonperturbative density regime from QCD first principles and develop many-body methods beyond the mean-field approximation. We will study the QCD-like theories at finite density which are free from sign problem and verify the validity of the effective theory and reliability of the many-body methods by comparing the theoretical predictions with some reliable lattice QCD results. Then we will study systematically the phase structure and physical properties of the strongly coupled quark matter in the nonperturbative density regime and predict new physical phenomena. This project will greatly advance the physics of QCD at finite density, and will provide solid ground for the studies of compact stars and baryon-rich heavy ion collisions.